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Definite Integration question

2003 · Shift 0 · Q83

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PYQ Library
JEE Main
Mathematics
Definite Integration
2003 · Shift 0 · Q83

Definite Integration question

2003 · Shift 0 · Q83

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f(x)

be a function satisfying

f'(x)=f(x)

with

f(0)=1

and

g(x)

be a function that satisfies

f\left( x \right) + g\left( x \right) = {x^2}

. Then the value of the integral

\int\limits_0^1 {f\left( x \right)g\left( x \right)dx,}

is

A
$e + {{{e^2}} \over 2} + {5 \over 2}$
B
$e - {{{e^2}} \over 2} - {5 \over 2}$
C
$e + {{{e^2}} \over 2} - {3 \over 2}$
D
$e - {{{e^2}} \over 2} - {3 \over 2}$

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